The function diversity.calc calculates the following diversity
measures
Margalef's Richness Index (\(D_{Margalef}\)) (Margalef 1973)
Menhinick's Index (\(D_{Menhinick}\)) (Menhinick 1964)
Berger–Parker Index (\(D_{BP}\)) (Berger and Parker 1970)
Reciprocal Berger–Parker Index (\(D_{BP_{R}}\)) (Magurran 2011)
Simpson's Index (\(d\)) (Simpson 1949; Peet 1974)
Simpson's Index of Diversity or Gini's Diversity Index or Gini-Simpson Index or Nei's Diversity Index or Nei's Variation Index (\(D\)) or Hurlbert’s probability of interspecific encounter (\(PIE\)) (Gini 1912, 1912; Greenberg 1956; Berger and Parker 1970; Hurlbert 1971; Nei 1973; Peet 1974)
Maximum Simpson's Index of Diversity or Maximum Nei's Diversity/Variation Index (\(D_{max}\)) (Hennink and Zeven 1990)
Simpson's Reciprocal Index or Hill's \(N_{2}\) (\(D_{R}\)) or Effective number of Species (\(ENS_{d}\)) (Williams 1964; Hill 1973)
Relative Simpson's Index of Diversity or Relative Nei's Diversity/Variation Index (\(D'\)) (Hennink and Zeven 1990)
Simpson’s evenness or equitability (\(D_{e}\)) (Pielou 1966; Hill 1973)
Shannon or Shannon-Weaver or Shannon-Wiener Diversity Index or Shannon entropy (\(H\)) (Shannon and Weaver 1949; Peet 1974)
Maximum Shannon-Weaver Diversity Index (\(H_{max}\)) (Hennink and Zeven 1990)
Relative Shannon-Weaver Diversity Index or Shannon Equitability Index (\(H'\)) or Pielou's Evenness (\(J\)) (Pielou 1966; Hennink and Zeven 1990)
Effective number of species for the Shannon - Weaver Diversity Index (\(ENS_{H}\)) or Hill's \(N_{1}\) (Macarthur 1965; Hill 1973)
Heip's Evenness Index (\(E_{Heip}\)) (Heip 1974)
McIntosh Diversity Index (\(D_{Mc}\)) (McIntosh 1967; Peet 1974)
McIntosh Evenness Index (\(E_{Mc}\)) (Pielou 1975)
Smith & Wilson's Evenness Index (\(E_{var}\)) (Smith and Wilson 1996)
Brillouin Diversity Index (\(D_{Brillouin}\)) (Brillouin 2013)
Rényi Entropy (\({}^q H_{Rényi}\)) (Renyi 1960)
Tsallis or HCDT Entropy (\({}^q H_{Tsallis}\)) (Havrda and Charvat 1967; Daroczy 1970; Tsallis 1988)
Hill Numbers (\({}^q D\)) (Hill 1973)
Usage
diversity.calc(x, base = exp(1), na.omit = TRUE)Arguments
- x
A factor vector of categories (e.g., species, traits). The frequency of each level is treated as the abundance of that category.
- base
The logarithm base to be used for computation of shannon family of diversity indices. Default is
exp(1).- na.omit
logical. If
TRUE, missing values (NA) are ignored and not included as a distinct factor level for computation. Default isTRUE.
Value
A list of different
- richness
The number of classes in
xor the richness.- margalef_index
Margalef's Richness Index (\(D_{Margalef}\)) (Margalef 1973)
- menhinick_index
Menhinick's Index (\(D_{Menhinick}\)) (Menhinick 1964)
- berger_parker
Berger–Parker Index (\(D_{BP}\)) (Berger and Parker 1970)
- berger_parker_reciprocal
Reciprocal Berger–Parker Index (\(D_{BP_{R}}\)) (Magurran 2011)
- simpson
Simpson's index (\(d\)) (Simpson 1949; Peet 1974)
- gini_simpson
Simpson's Index of Diversity or Gini's Diversity Index or Gini-Simpson Index or Nei's Diversity Index or Nei's Variation Index (\(D\)) or Hurlbert’s probability of interspecific encounter (\(PIE\)) (Gini 1912, 1912; Greenberg 1956; Berger and Parker 1970; Hurlbert 1971; Nei 1973; Peet 1974)
- simpson_max
Maximum Simpson's Index of Diversity or Maximum Nei's Diversity/Variation Index (\(D_{max}\)) (Hennink and Zeven 1990)
- simpson_reciprocal
Simpson's Reciprocal Index or Hill's \(N_{2}\) (\(D_{R}\)) or Effective number of Species (\(ENS_{d}\)) (Williams 1964; Hill 1973)
- simpson_relative
Relative Simpson's Index of Diversity or Relative Nei's Diversity/Variation Index (\(D'\)) (Hennink and Zeven 1990)
- simpson_evenness
Simpson’s evenness or equitability (\(D_{e}\)) (Pielou 1966; Hill 1973)
- shannon
Shannon or Shannon-Weaver or Shannon-Wiener Diversity Index or Shannon entropy (\(H\)) (Shannon and Weaver 1949; Peet 1974)
- shannon_max
Maximum Shannon-Weaver Diversity Index (\(H_{max}\)) (Hennink and Zeven 1990)
- shannon_relative
Relative Shannon-Weaver Diversity Index or Shannon Equitability Index (\(H'\)) or Pielou's Evenness (\(J\)) (Pielou 1966; Hennink and Zeven 1990)
- shannon_ens
Effective number of species for the Shannon - Weaver Diversity Index (\(ENS_{H}\)) or Hill's \(N_{1}\) (Macarthur 1965; Hill 1973)
- heip_evenness
Heip's Evenness Index (\(E_{Heip}\)) (Heip 1974)
- mcintosh_diversity
McIntosh Diversity Index (\(D_{Mc}\)) (McIntosh 1967; Peet 1974)
- mcintosh_evenness
McIntosh Evenness Index (\(E_{Mc}\)) (Pielou 1975)
- smith_wilson
Smith & Wilson's Evenness Index (\(E_{var}\)) (Smith and Wilson 1996)
- brillouin_index
Brillouin Diversity Index (Brillouin 2013)
- renyi_entropy_0
Rényi Entropy of order 0 (Renyi 1960)
- renyi_entropy_1
Rényi Entropy of order 1
- renyi_entropy_2
Rényi Entropy of order 2
- tsallis_entropy_0
Tsallis Entropy of order 0 (Havrda and Charvat 1967; Daroczy 1970; Tsallis 1988)
- tsallis_entropy_1
Tsallis Entropy of order 1
- tsallis_entropy_2
Tsallis Entropy of order 2
- hill_number_0
Hill Number of order 0 (\({}^0 D\)) (Hill 1973)
- hill_number_1
Hill Number of order 1 (\({}^1 D\))
- hill_number_2
Hill Number of order 2 (\({}^2 D\))
Details
The diversity indices implemented in diversity.calc
are computed as follows.
Richness Indices
The number of classes of a phenotypic trait (or species richness) (\(k\)) can be described by adjusting for sample size (\(N\)) in Margalef's Richness Index (\(D_{Margalef}\)) (Margalef 1973) and Menhinick's Index (\(D_{Menhinick}\)) (Menhinick 1964)
These are computed as follows.
\[D_{Margalef} = \frac{k - 1}{\ln(N)}\]
\[D_{Menhinick} = \frac{k}{\sqrt{N}}\]
Berger–Parker Index
This is the is the proportion of individuals belonging to the most abundant class in a trait (or species in a community) and is computed as below.
\[D_{BP} = \max(p_i)\]
Where, \(p_{i}\) denotes the proportion/fraction/frequency of accessions in the \(i\)th phenotypic class for a trait (or number of individuals in the \(i\)th species).
It's reciprocal estimates the relative diversity of this class.
\[D_{BP_{R}} = \frac{1}{D_{BP}}\]
Simpson's and Related Indices
Simpson's index (\(d\)) which estimates the probability that two accessions randomly selected will belong to the same phenotypic class of a trait (or species in a community), is computed as follows (Simpson 1949; Peet 1974) .
\[d = \sum_{i = 1}^{k}p_{i}^{2}\]
Where, \(k\) is the number of phenotypic classes for the trait (or number of species in the community).
The value of \(d\) can range from 0 to 1 with 0 representing maximum diversity and 1, no diversity.
\(d\) is subtracted from 1 to give Simpson's index of diversity (\(D\)) (Greenberg 1956; Berger and Parker 1970; Hurlbert 1971; Peet 1974; Hennink and Zeven 1990) originally suggested by Gini (1912, 1912) and described in literature as Gini's diversity index or Gini-Simpson index. It is the same as Nei's diversity index or Nei's variation index (Nei 1973; Hennink and Zeven 1990) . Greater the value of \(D\), greater the diversity with a range from 0 to 1.
\[D = 1 - d\]
The maximum value of \(D\), \(D_{max}\) occurs when accessions are uniformly distributed across the phenotypic classes (or individuals are uniformly distributed across species in a community) and is computed as follows (Hennink and Zeven 1990) .
\[D_{max} = 1 - \frac{1}{k}\]
Reciprocal of \(d\) gives the Simpson's reciprocal index (\(D_{R}\)) (Williams 1964; Hennink and Zeven 1990) and can range from 1 to \(k\). This was also described in Hill (1973) as \(N_{2}\) or as Effective number of Species (or classes) (\(ENS_{d}\)).
\[D_{R} = \frac{1}{d}\]
Relative Simpson's index of diversity or Relative Nei's diversity/variation index (\(H'\)) (Hennink and Zeven 1990) is defined as follows (Peet 1974) .
\[D' = \frac{D}{D_{max}}\]
Simpson’s evenness or equitability (\(D_{e}\) is described as follows (Pielou 1966; Hill 1973) .
\[D_{e} = \frac{1}{d \cdot k}\]
Shannon-Weaver and Related Indices
An index of information \(H\), was described by Shannon and Weaver (1949) as follows.
\[H = -\sum_{i=1}^{k}p_{i} \log_{2}(p_{i})\]
\(H\) is described as Shannon or Shannon-Weaver or Shannon-Wiener diversity index or Shannon entropy in literature (Shannon and Weaver 1949; Peet 1974) .
Alternatively, \(H\) is also computed using natural logarithm instead of logarithm to base 2.
\[H = -\sum_{i=1}^{k}p_{i} \ln(p_{i})\]
The maximum value of \(H\) (\(H_{max}\)) is \(\ln(k)\). This value occurs when each phenotypic class for a trait has the same proportion of accessions (or each species in a community has the same proportion of individuals) (Hennink and Zeven 1990) .
\[H_{max} = \log_{2}(k)\;\; \textrm{OR} \;\; H_{max} = \ln(k)\]
The relative Shannon-Weaver diversity index or Shannon equitability index (\(H'\)) or Pielou's Evenness (\(J\)) is the Shannon diversity index (\(I\)) divided by the maximum diversity (\(H_{max}\)) (Pielou 1966; Hennink and Zeven 1990) .
\[H' = \frac{H}{H_{max}}\]
Macarthur (1965) described the Effective number of species (or classes) for the Shannon index (\(ENS_{H}\)) as follows.
\[ENS_{H} = e^{H}\]
Heip’s index or Heip's Evenness index is a transformation of the Shannon–Wiener diversity index that standardizes it relative to number of classes in the trait (or species richness) and is computed as follows (Heip 1974) .
\[E_{Heip} = \frac{e^{H} - 1}{k - 1}\]
McIntosh's Measure of Diversity
A similar index of diversity was described by McIntosh (1967) as follows (\(D_{Mc}\)) (Peet 1974) .
\[D_{Mc} = \frac{N - \sqrt{\sum_{i=1}^{k}n_{i}^2}}{N - \sqrt{N}}\]
Where, \(n_{i}\) denotes the number of accessions in the \(i\)th phenotypic class for a trait (or number of individuals in the \(i\)th species in the community) and \(N\) is the total number of accessions so that \(p_{i} = {n_{i}}/{N}\).
An additional measure of evenness was proposed by Pielou (1975) as follows.
\[E_{Mc} = \frac{N - \sqrt{\sum_{i=1}^{k}n_{i}^2}}{N - \frac{N}{\sqrt{S}}}\]
Smith & Wilson's Evenness Index
This index measures how equally are accessions/genotypes distributed among different trait classes (or individuals individuals are distributed among different species in a community). This is less sensitive to rare classes or species and is computed as follows.
\[E_{var} = 1 - \frac{2}{\pi} \arctan{\left ( \frac{1}{k} \sum_{i=1}^{k}(\ln{n_{i} - \overline{\ln{n}}})^{2} \right )}\]
Brillouin Diversity Index
This is an information-theoretic measure appropriate for complete censuses and is computed as follows (Brillouin 2013) .
\[H_{B} = \frac{\ln(N!) - \sum \ln(n_i!)}{N}\]
Parametric Indices
Parametric indices, also known as multivariate or compound indices, use a sensitivity parameter (\(q\)) to weigh frequent and rare classes within a trait (or common or rare species within a community).
The Rényi entropy extends several entropy measures, including Shannon entropy, and is computed as follows (Renyi 1960) .
\[{}^q H_{Rényi} = \frac{1}{1-q} \ln \sum_{i=1}^{k} p_{i}^{q} , \quad q \ge 0, q \neq 1\]
It is more frequently computed using natural logarithm instead of logarithm to base 2. The index is undefined for (\(q = 1\)), but Shannon entropy is as a limiting case.
Tsallis proposed a similar measure, the HCDT or Tsallis entropy (Havrda and Charvat 1967; Daroczy 1970; Tsallis 1988) , which matches species richness for \(q = 0\), Shannon entropy \(q = 1\), and the Gini-Simpson index for \(q = 2\).
\[{}^q H_{Tsallis} = \frac{1}{q - 1} \left ( 1 - \sum_{i=1}^{k} p_i^q \right ), \quad q \ge 0, q \neq 1\]
Hill showed that species richness, Shannon entropy, and Simpson's index are all related diversity indices, collectively known as Hill numbers which is defined as below (Hill 1973) .
\[{}^q D = {\left ( \sum_{i=1}^{k} p_{i}^{q} \right )}^{\frac{1}{1-q}} , \quad q \ge 0, q \neq 1\]
Where,
\[{}^0 D = k\]
\[{}^1 D = e^{H}\]
\[{}^2 D = D_{R}\]
References
Berger WH, Parker FL (1970).
“Diversity of planktonic foraminifera in deep-sea sediments.”
Science, 168(3937), 1345–1347.
Brillouin L (2013).
Science and information theory, Dover edition.
Dover Publications, Inc., Mineola, New York.
ISBN 978-0-486-31641-3.
Daroczy Z (1970).
“Generalized information functions.”
Information and Control, 16(1), 36–51.
Gini C (1912).
Variabilita e Mutabilita. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. [Fasc. I.].
Tipogr. di P. Cuppini, Bologna.
Gini C (1912).
“Variabilita e mutabilita.”
In Pizetti E, Salvemini T (eds.), Memorie di Metodologica Statistica.
Liberia Eredi Virgilio Veschi, Roma, Italy.
Greenberg JH (1956).
“The measurement of linguistic diversity.”
Language, 32(1), 109.
Havrda J, Charvat F (1967).
“Quantification method of classification processes. Concept of structural <p>α</p>-entropy.”
Kybernetika, 3(1), (30)–35.
Heip C (1974).
“A new index measuring evenness.”
Journal of the Marine Biological Association of the United Kingdom, 54(3), 555–557.
Hennink S, Zeven AC (1990).
“The interpretation of Nei and Shannon-Weaver within population variation indices.”
Euphytica, 51(3), 235–240.
Hill MO (1973).
“Diversity and evenness: A unifying notation and its consequences.”
Ecology, 54(2), 427–432.
Hurlbert SH (1971).
“The nonconcept of species diversity: a critique and alternative parameters.”
Ecology, 52(4), 577–586.
Macarthur RH (1965).
“Patterns of species diversity.”
Biological Reviews, 40(4), 510–533.
Magurran AE (2011).
Measuring biological diversity, 9 [Nachdr.] edition.
Blackwell, Malden, Mass.
ISBN 978-0-632-05633-0.
Margalef R (1973).
“Information theory in ecology.”
International Journal of General Systems, 3, 36–71.
McIntosh RP (1967).
“An index of diversity and the relation of certain concepts to diversity.”
Ecology, 48(3), 392–404.
Menhinick EF (1964).
“A comparison of some species-individuals diversity indices applied to samples of field insects.”
Ecology, 45(4), 859–861.
Nei M (1973).
“Analysis of gene diversity in subdivided populations.”
Proceedings of the National Academy of Sciences, 70(12), 3321–3323.
Peet RK (1974).
“The measurement of species diversity.”
Annual Review of Ecology and Systematics, 5(1), 285–307.
Pielou EC (1966).
“The measurement of diversity in different types of biological collections.”
Journal of Theoretical Biology, 13, 131–144.
Pielou EC (1975).
Ecological diversity.
New York : Wiley.
ISBN 978-0-471-68925-6.
Renyi A (1960).
“On measures of entropy and information.”
In Neyman J (ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (June 20-July 30 1960), Volume I: Contributions to the Theory of Statistics, 547–561.
University of California Press.
Shannon CE, Weaver W (1949).
The Mathematical Theory of Communication, number v. 2 in The Mathematical Theory of Communication.
University of Illinois Press.
Simpson EH (1949).
“Measurement of diversity.”
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Smith B, Wilson JB (1996).
“A consumer's guide to evenness indices.”
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Tsallis C (1988).
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Williams CB (1964).
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Examples
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Qualitative trait data ----
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
library(EvaluateCore)
pdata <- cassava_CC
qual <- c("CUAL", "LNGS", "PTLC", "DSTA", "LFRT", "LBTEF", "CBTR", "NMLB",
"ANGB", "CUAL9M", "LVC9M", "TNPR9M", "PL9M", "STRP", "STRC",
"PSTR")
# Convert qualitative data columns to factor
pdata[, qual] <- lapply(pdata[, qual], as.factor)
# Get diversity measures
diversity.calc(x = pdata$CUAL)
#> $richness
#> [1] 4
#>
#> $margalef_index
#> [1] 0.5854842
#>
#> $menhinick_index
#> [1] 0.3086067
#>
#> $berger_parker
#> [1] 0.5297619
#>
#> $berger_parker_reciprocal
#> [1] 1.88764
#>
#> $simpson
#> [1] 0.3784722
#>
#> $gini_simpson
#> [1] 0.6215278
#>
#> $simpson_max
#> [1] 0.75
#>
#> $simpson_reciprocal
#> [1] 2.642202
#>
#> $simpson_relative
#> [1] 0.8287037
#>
#> $simpson_evenness
#> [1] 0.4022346
#>
#> $shannon
#> [1] 1.113994
#>
#> $shannon_max
#> [1] 1.386294
#>
#> $shannon_relative
#> [1] 0.803577
#>
#> $shannon_ens
#> [1] 3.046503
#>
#> $heip_evenness
#> [1] 1.329531
#>
#> $mcintosh_diversity
#> [1] 0.4169689
#>
#> $mcintosh_evenness
#> [1] 0.7695981
#>
#> $smith_wilson
#> [1] 0.4591224
#>
#> $brillouin_index
#> [1] 1.072686
#>
#> $renyi_entropy_0
#> [1] 1.386294
#>
#> $renyi_entropy_1
#> [1] 1.113994
#>
#> $renyi_entropy_2
#> [1] 0.9716126
#>
#> $tsallis_entropy_0
#> [1] 3
#>
#> $tsallis_entropy_1
#> [1] 1.113994
#>
#> $tsallis_entropy_2
#> [1] 0.6215278
#>
#> $hill_number_0
#> [1] 4
#>
#> $hill_number_1
#> [1] 3.046503
#>
#> $hill_number_2
#> [1] 2.642202
#>
# Get diversity measures for multiple qualitative traits
div_out1 <- lapply(pdata[, qual], diversity.calc)
do.call(rbind, div_out1)
#> richness margalef_index menhinick_index berger_parker
#> CUAL 4 0.5854842 0.3086067 0.5297619
#> LNGS 3 0.3903228 0.231455 0.4285714
#> PTLC 5 0.7806456 0.3857584 0.5892857
#> DSTA 5 0.7806456 0.3857584 0.4404762
#> LFRT 4 0.5854842 0.3086067 0.5238095
#> LBTEF 6 0.975807 0.46291 0.2559524
#> CBTR 3 0.3903228 0.231455 0.5595238
#> NMLB 9 1.561291 0.6943651 0.3214286
#> ANGB 4 0.5854842 0.3086067 0.452381
#> CUAL9M 5 0.7806456 0.3857584 0.3333333
#> LVC9M 5 0.7806456 0.3857584 0.5
#> TNPR9M 5 0.7806456 0.3857584 0.3214286
#> PL9M 2 0.1951614 0.1543033 0.5119048
#> STRP 4 0.5854842 0.3086067 0.3392857
#> STRC 2 0.1951614 0.1543033 0.5952381
#> PSTR 2 0.1951614 0.1543033 0.6666667
#> berger_parker_reciprocal simpson gini_simpson simpson_max
#> CUAL 1.88764 0.3784722 0.6215278 0.75
#> LNGS 2.333333 0.3877551 0.6122449 0.6666667
#> PTLC 1.69697 0.4213435 0.5786565 0.8
#> DSTA 2.27027 0.3035006 0.6964994 0.8
#> LFRT 1.909091 0.4265873 0.5734127 0.75
#> LBTEF 3.906977 0.2005385 0.7994615 0.8333333
#> CBTR 1.787234 0.4872449 0.5127551 0.6666667
#> NMLB 3.111111 0.1980584 0.8019416 0.8888889
#> ANGB 2.210526 0.3421202 0.6578798 0.75
#> CUAL9M 3 0.2880527 0.7119473 0.8
#> LVC9M 2 0.3886763 0.6113237 0.8
#> TNPR9M 3.111111 0.2218679 0.7781321 0.8
#> PL9M 1.953488 0.5002834 0.4997166 0.5
#> STRP 2.947368 0.3118622 0.6881378 0.75
#> STRC 1.68 0.5181406 0.4818594 0.5
#> PSTR 1.5 0.5555556 0.4444444 0.5
#> simpson_reciprocal simpson_relative simpson_evenness shannon
#> CUAL 2.642202 0.8287037 0.4022346 1.113994
#> LNGS 2.578947 0.9183673 0.5444444 1.004242
#> PTLC 2.37336 0.7233206 0.3456282 1.113785
#> DSTA 3.294887 0.8706243 0.2871503 1.349228
#> LFRT 2.344186 0.7645503 0.4359862 0.9661827
#> LBTEF 4.986572 0.9593537 0.2084737 1.651889
#> CBTR 2.052356 0.7691327 0.6500829 0.778669
#> NMLB 5.049016 0.9021843 0.1385526 1.775015
#> ANGB 2.922949 0.8771731 0.3800086 1.176272
#> CUAL9M 3.471587 0.8899341 0.2809197 1.335612
#> LVC9M 2.572835 0.7641546 0.3271589 1.10697
#> TNPR9M 4.507186 0.9726651 0.2570258 1.557711
#> PL9M 1.998867 0.9994331 1.000567 0.6928637
#> STRP 3.206544 0.917517 0.3632994 1.21246
#> STRC 1.929978 0.9637188 1.037647 0.6748953
#> PSTR 1.8 0.8888889 1.125 0.6365142
#> shannon_max shannon_relative shannon_ens heip_evenness
#> CUAL 1.386294 0.803577 3.046503 1.329531
#> LNGS 1.098612 0.9141009 2.729839 1.629034
#> PTLC 1.609438 0.6920334 3.045865 0.9967717
#> DSTA 1.609438 0.8383227 3.85445 1.501076
#> LFRT 1.386294 0.6969535 2.627894 1.010189
#> LBTEF 1.791759 0.9219369 5.216826 1.967847
#> CBTR 1.098612 0.7087751 2.178571 1.037618
#> NMLB 2.197225 0.807844 5.900367 1.493279
#> ANGB 1.386294 0.8485006 3.242263 1.485852
#> CUAL9M 1.609438 0.8298622 3.802321 1.467013
#> LVC9M 1.609438 0.6877994 3.025179 0.9845744
#> TNPR9M 1.609438 0.9678601 4.74794 2.115542
#> PL9M 0.6931472 0.999591 1.999433 1.71717
#> STRP 1.386294 0.8746048 3.361743 1.583352
#> STRC 0.6931472 0.9736681 1.963827 1.647638
#> PSTR 0.6931472 0.9182958 1.889882 1.505018
#> mcintosh_diversity mcintosh_evenness smith_wilson brillouin_index
#> CUAL 0.4169689 0.7695981 0.4591224 1.072686
#> LNGS 0.4088431 0.8927017 0.6401521 0.9736063
#> PTLC 0.3802252 0.6347663 0.4467806 1.06311
#> DSTA 0.4866359 0.8124135 0.5123229 1.294889
#> LFRT 0.3758619 0.693727 0.3336841 0.9291107
#> LBTEF 0.5983483 0.9331358 0.5031023 1.584527
#> CBTR 0.327216 0.7144704 0.3314674 0.7525541
#> NMLB 0.6013583 0.8324437 0.3647054 1.686068
#> ANGB 0.4497918 0.8301792 0.5028364 1.133948
#> CUAL9M 0.5020268 0.8381077 0.4522341 1.282613
#> LVC9M 0.408042 0.6812051 0.3707252 1.058812
#> TNPR9M 0.5731943 0.9569183 0.7843173 1.49946
#> PL9M 0.3171624 0.9993158 0.9785679 0.6762626
#> STRP 0.4784684 0.8831074 0.4699856 1.170253
#> STRC 0.3036037 0.9565949 0.8305121 0.6584021
#> PSTR 0.2759327 0.869409 0.7098798 0.6202605
#> renyi_entropy_0 renyi_entropy_1 renyi_entropy_2 tsallis_entropy_0
#> CUAL 1.386294 1.113994 0.9716126 3
#> LNGS 1.098612 1.004242 0.9473813 2
#> PTLC 1.609438 1.113785 0.8643068 4
#> DSTA 1.609438 1.349228 1.192372 4
#> LFRT 1.386294 0.9661827 0.8519382 3
#> LBTEF 1.791759 1.651889 1.606749 5
#> CBTR 1.098612 0.778669 0.7189884 2
#> NMLB 2.197225 1.775015 1.619193 8
#> ANGB 1.386294 1.176272 1.072593 3
#> CUAL9M 1.609438 1.335612 1.244612 4
#> LVC9M 1.609438 1.10697 0.9450084 4
#> TNPR9M 1.609438 1.557711 1.505673 4
#> PL9M 0.6931472 0.6928637 0.6925804 1
#> STRP 1.386294 1.21246 1.165194 3
#> STRC 0.6931472 0.6748953 0.6575087 1
#> PSTR 0.6931472 0.6365142 0.5877867 1
#> tsallis_entropy_1 tsallis_entropy_2 hill_number_0 hill_number_1
#> CUAL 1.113994 0.6215278 4 3.046503
#> LNGS 1.004242 0.6122449 3 2.729839
#> PTLC 1.113785 0.5786565 5 3.045865
#> DSTA 1.349228 0.6964994 5 3.85445
#> LFRT 0.9661827 0.5734127 4 2.627894
#> LBTEF 1.651889 0.7994615 6 5.216826
#> CBTR 0.778669 0.5127551 3 2.178571
#> NMLB 1.775015 0.8019416 9 5.900367
#> ANGB 1.176272 0.6578798 4 3.242263
#> CUAL9M 1.335612 0.7119473 5 3.802321
#> LVC9M 1.10697 0.6113237 5 3.025179
#> TNPR9M 1.557711 0.7781321 5 4.74794
#> PL9M 0.6928637 0.4997166 2 1.999433
#> STRP 1.21246 0.6881378 4 3.361743
#> STRC 0.6748953 0.4818594 2 1.963827
#> PSTR 0.6365142 0.4444444 2 1.889882
#> hill_number_2
#> CUAL 2.642202
#> LNGS 2.578947
#> PTLC 2.37336
#> DSTA 3.294887
#> LFRT 2.344186
#> LBTEF 4.986572
#> CBTR 2.052356
#> NMLB 5.049016
#> ANGB 2.922949
#> CUAL9M 3.471587
#> LVC9M 2.572835
#> TNPR9M 4.507186
#> PL9M 1.998867
#> STRP 3.206544
#> STRC 1.929978
#> PSTR 1.8
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Species abundance data ----
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
library(vegan)
#> Loading required package: permute
data(dune)
abundance_site1 <- unlist(dune[1, ])
abundance_site1[abundance_site1 != 0]
#> Achimill Elymrepe Lolipere Poaprat Poatriv
#> 1 4 7 4 2
# Convert to raw counts for use in diversity.calc using rep
abundance_site1_raw <- factor(rep(names(abundance_site1),
times = abundance_site1))
# Get diversity measures
diversity.calc(x = abundance_site1_raw)
#> $richness
#> [1] 5
#>
#> $margalef_index
#> [1] 1.383905
#>
#> $menhinick_index
#> [1] 1.178511
#>
#> $berger_parker
#> [1] 0.3888889
#>
#> $berger_parker_reciprocal
#> [1] 2.571429
#>
#> $simpson
#> [1] 0.2654321
#>
#> $gini_simpson
#> [1] 0.7345679
#>
#> $simpson_max
#> [1] 0.8
#>
#> $simpson_reciprocal
#> [1] 3.767442
#>
#> $simpson_relative
#> [1] 0.9182099
#>
#> $simpson_evenness
#> [1] 0.2722689
#>
#> $shannon
#> [1] 1.440482
#>
#> $shannon_max
#> [1] 1.609438
#>
#> $shannon_relative
#> [1] 0.8950216
#>
#> $shannon_ens
#> [1] 4.22273
#>
#> $heip_evenness
#> [1] 1.74747
#>
#> $mcintosh_diversity
#> [1] 0.6343064
#>
#> $mcintosh_evenness
#> [1] 0.8770096
#>
#> $smith_wilson
#> [1] 0.5900996
#>
#> $brillouin_index
#> [1] 1.156724
#>
#> $renyi_entropy_0
#> [1] 1.609438
#>
#> $renyi_entropy_1
#> [1] 1.440482
#>
#> $renyi_entropy_2
#> [1] 1.326396
#>
#> $tsallis_entropy_0
#> [1] 4
#>
#> $tsallis_entropy_1
#> [1] 1.440482
#>
#> $tsallis_entropy_2
#> [1] 0.7345679
#>
#> $hill_number_0
#> [1] 5
#>
#> $hill_number_1
#> [1] 4.22273
#>
#> $hill_number_2
#> [1] 3.767442
#>
# Convert multiple site abundance data to raw counts
abundance_site_raw <- apply(dune, 1, function(x) {
factor(rep(names(x), times = x))
})
# Get diversity measures for multiple sites
div_out2 <- lapply(abundance_site_raw, diversity.calc)
do.call(rbind, div_out2)
#> richness margalef_index menhinick_index berger_parker
#> 1 5 1.383905 1.178511 0.3888889
#> 2 10 2.407917 1.543033 0.1666667
#> 3 10 2.439765 1.581139 0.175
#> 4 13 3.152368 1.937926 0.1777778
#> 5 14 3.456344 2.13498 0.1395349
#> 6 11 2.583178 1.587713 0.125
#> 7 13 3.25302 2.05548 0.15
#> 8 12 2.981935 1.897367 0.125
#> 9 13 3.210557 2.005944 0.1428571
#> 10 12 2.924598 1.829983 0.1395349
#> 11 9 2.308312 1.59099 0.21875
#> 12 9 2.250131 1.521278 0.2285714
#> 13 10 2.573997 1.740777 0.2727273
#> 14 7 1.887948 1.428869 0.25
#> 15 8 2.232503 1.668115 0.2173913
#> 16 8 2.001998 1.392621 0.2424242
#> 17 7 2.215616 1.807392 0.2666667
#> 18 9 2.427305 1.732051 0.2222222
#> 19 9 2.329653 1.616448 0.1935484
#> 20 8 2.038447 1.436842 0.1612903
#> berger_parker_reciprocal simpson gini_simpson simpson_max
#> 1 2.571429 0.2654321 0.7345679 0.8
#> 2 6 0.1099773 0.8900227 0.9
#> 3 5.714286 0.12125 0.87875 0.9
#> 4 5.625 0.09925926 0.9007407 0.9230769
#> 5 7.166667 0.08599243 0.9140076 0.9285714
#> 6 8 0.09982639 0.9001736 0.9090909
#> 7 6.666667 0.0925 0.9075 0.9230769
#> 8 8 0.09125 0.90875 0.9166667
#> 9 7 0.08843537 0.9115646 0.9230769
#> 10 7.166667 0.09680909 0.9031909 0.9166667
#> 11 4.571429 0.1328125 0.8671875 0.8888889
#> 12 4.375 0.1314286 0.8685714 0.8888889
#> 13 3.666667 0.1478421 0.8521579 0.9
#> 14 4 0.1666667 0.8333333 0.8571429
#> 15 4.6 0.1493384 0.8506616 0.875
#> 16 4.125 0.1570248 0.8429752 0.875
#> 17 3.75 0.1644444 0.8355556 0.8571429
#> 18 4.5 0.138546 0.861454 0.8888889
#> 19 5.166667 0.1259105 0.8740895 0.8888889
#> 20 6.2 0.132154 0.867846 0.875
#> simpson_reciprocal simpson_relative simpson_evenness shannon shannon_max
#> 1 3.767442 0.9182099 0.2722689 1.440482 1.609438
#> 2 9.092784 0.9889141 0.1123567 2.252516 2.302585
#> 3 8.247423 0.9763889 0.113798 2.193749 2.302585
#> 4 10.07463 0.9758025 0.0853998 2.426779 2.564949
#> 5 11.62893 0.9843158 0.07814877 2.544421 2.639057
#> 6 10.01739 0.990191 0.1009906 2.345946 2.397895
#> 7 10.81081 0.983125 0.08476372 2.471733 2.564949
#> 8 10.9589 0.9913636 0.09170105 2.434898 2.484907
#> 9 11.30769 0.9875283 0.08438576 2.493568 2.564949
#> 10 10.32961 0.9852992 0.09226547 2.398613 2.484907
#> 11 7.529412 0.9755859 0.1281281 2.106065 2.197225
#> 12 7.608696 0.9771429 0.127924 2.114495 2.197225
#> 13 6.763975 0.9468422 0.1173491 2.099638 2.302585
#> 14 6 0.9722222 0.1714286 1.86368 1.94591
#> 15 6.696203 0.9721847 0.1469444 1.979309 2.079442
#> 16 6.368421 0.9634002 0.1482843 1.959795 2.079442
#> 17 6.081081 0.9748148 0.1709726 1.876274 1.94591
#> 18 7.217822 0.9691358 0.1289809 2.079387 2.197225
#> 19 7.942149 0.9833507 0.1271164 2.134024 2.197225
#> 20 7.566929 0.991824 0.1440348 2.04827 2.079442
#> shannon_relative shannon_ens heip_evenness mcintosh_diversity
#> 1 0.8950216 4.22273 1.74747 0.6343064
#> 2 0.9782554 9.51164 2.753606 0.7903209
#> 3 0.9527332 8.968777 2.520738 0.7742024
#> 4 0.9461313 11.32235 2.67933 0.8049388
#> 5 0.9641403 12.73586 2.944944 0.8339282
#> 6 0.9783356 10.44315 2.85028 0.7994354
#> 7 0.9636577 11.84296 2.864442 0.8265511
#> 8 0.9798749 11.41465 2.958414 0.8290003
#> 9 0.9721705 12.10439 2.958778 0.830817
#> 10 0.9652727 11.00789 2.802893 0.8128109
#> 11 0.9585114 8.215847 2.484002 0.7720451
#> 12 0.9623483 8.285403 2.515928 0.7671394
#> 13 0.911861 8.163211 2.186597 0.7452246
#> 14 0.9577421 6.44742 2.285477 0.7435226
#> 15 0.9518463 7.237739 2.340544 0.7751964
#> 16 0.9424621 7.097871 2.271604 0.7309845
#> 17 0.9642139 6.529129 2.330436 0.8014042
#> 18 0.9463699 7.999566 2.385495 0.7773914
#> 19 0.9712362 8.448796 2.591391 0.7864035
#> 20 0.9850099 7.754478 2.600327 0.7758096
#> mcintosh_evenness smith_wilson brillouin_index renyi_entropy_0
#> 1 0.8770096 0.5900996 1.156724 1.609438
#> 2 0.9774771 0.7851387 1.930319 2.302585
#> 3 0.9532272 0.6925466 1.86802 2.302585
#> 4 0.947825 0.6687728 2.056517 2.564949
#> 5 0.9645393 0.7407779 2.132228 2.639057
#> 6 0.9793242 0.7749676 2.02765 2.397895
#> 7 0.9629308 0.7433868 2.06382 2.564949
#> 8 0.9811605 0.7830292 2.047512 2.484907
#> 9 0.9722815 0.7640758 2.095951 2.564949
#> 10 0.968416 0.7006824 2.035221 2.484907
#> 11 0.9533483 0.733735 1.75707 2.197225
#> 12 0.9562038 0.7463774 1.784664 2.197225
#> 13 0.9001501 0.6387338 1.740005 2.302585
#> 14 0.951315 0.7317419 1.524661 1.94591
#> 15 0.9491221 0.6916521 1.590951 2.079442
#> 16 0.9339309 0.6971933 1.654509 2.079442
#> 17 0.9557051 0.7576586 1.417032 1.94591
#> 18 0.9416736 0.686416 1.693929 2.197225
#> 19 0.9677419 0.7738024 1.774003 2.197225
#> 20 0.9845671 0.814859 1.720004 2.079442
#> renyi_entropy_1 renyi_entropy_2 tsallis_entropy_0 tsallis_entropy_1
#> 1 1.440482 1.326396 4 1.440482
#> 2 2.252516 2.207481 9 2.252516
#> 3 2.193749 2.109901 9 2.193749
#> 4 2.426779 2.31002 12 2.426779
#> 5 2.544421 2.453496 13 2.544421
#> 6 2.345946 2.304323 10 2.345946
#> 7 2.471733 2.380547 12 2.471733
#> 8 2.434898 2.394152 11 2.434898
#> 9 2.493568 2.425483 12 2.493568
#> 10 2.398613 2.335014 11 2.398613
#> 11 2.106065 2.018817 8 2.106065
#> 12 2.114495 2.029292 8 2.114495
#> 13 2.099638 1.911611 9 2.099638
#> 14 1.86368 1.791759 6 1.86368
#> 15 1.979309 1.901541 7 1.979309
#> 16 1.959795 1.851352 7 1.959795
#> 17 1.876274 1.805182 6 1.876274
#> 18 2.079387 1.976553 8 2.079387
#> 19 2.134024 2.072184 8 2.134024
#> 20 2.04827 2.023787 7 2.04827
#> tsallis_entropy_2 hill_number_0 hill_number_1 hill_number_2
#> 1 0.7345679 5 4.22273 3.767442
#> 2 0.8900227 10 9.51164 9.092784
#> 3 0.87875 10 8.968777 8.247423
#> 4 0.9007407 13 11.32235 10.07463
#> 5 0.9140076 14 12.73586 11.62893
#> 6 0.9001736 11 10.44315 10.01739
#> 7 0.9075 13 11.84296 10.81081
#> 8 0.90875 12 11.41465 10.9589
#> 9 0.9115646 13 12.10439 11.30769
#> 10 0.9031909 12 11.00789 10.32961
#> 11 0.8671875 9 8.215847 7.529412
#> 12 0.8685714 9 8.285403 7.608696
#> 13 0.8521579 10 8.163211 6.763975
#> 14 0.8333333 7 6.44742 6
#> 15 0.8506616 8 7.237739 6.696203
#> 16 0.8429752 8 7.097871 6.368421
#> 17 0.8355556 7 6.529129 6.081081
#> 18 0.861454 9 7.999566 7.217822
#> 19 0.8740895 9 8.448796 7.942149
#> 20 0.867846 8 7.754478 7.566929